Math480: Sample Questions on Chapter 11
Problem 1 Find all eigenvalues and eigenfunctions. Normalize the
eigenfunctions if possible :
y00 +λy = 0; y(0) + y0(0) = 0, y(1) + y0(1) = 0.
Problem 2 Expand the function f(x) = xon [0,1] into a Fourier
series using the functions obtained in Problem 1.
Problem 3 Convert the Chebyshev equation
(1 −x2)y00
−xy0+α2y= 0,
into the canonical form of the Sturm-Liouville problem.
Problem 4 Do Problem #17 p.663
Problem 5 On nonhomogeneous problems practice finding solutions
on these exercises: #3,11,20,22
Problem 6 Do the homework on Sec 11.4: 1 and 11.5: 2,3,7
